Intensive Calculus for the Physical and Life Sciences - Math 33

Fall ‘99 - Professor Anderson

What is Intensive Calculus?

Intensive Calculus (Math 33) uses the same textbook and covers exactly the same material (roughly the first six chapters of the text) as Calculus for the Physical and Life Sciences (Math 31). Both are first calculus courses - we do not assume that you have any calculus background. Both are intended for students planning to major in mathematics or the sciences. (Another first calculus course, Math 25-26, is intended for students majoring in the social sciences.) The most obvious difference between Math 31 and Math 33 is that Intensive Calculus meets 5 days a week rather than 4. The extra hour allows us to spend a little more time on difficult topics, to review precalculus topics if necessary, to spend more time discussing homework problems, and to work on problems in groups. It is designed for those who feel that they could benefit from the extra class time.

Text: Calculus, Hughes-Hallet et al., 2nd ed., Wiley 1998.

Topics: The first three weeks or so are devoted to chapter 1, a review of various types of functions (linear, exponential, logarithms, polynomials, rational functions, trig functions) and concepts such as graphs, compositions and inverses of functions.

In chapter 2, the concept of the derivative of a function is introduced. The emphasis here is on understanding the concept and various interpretations of the derivative - velocity, slope of the tangent line, rate of change, etc. Then we will skip to chapter 4, which derives formulas for computing the derivatives of the functions studied in chapter 1.

Next, in chapter 5, we will see several applications of differentiation (the process of finding the derivative of a function): optimization (min/max) problems, finding solutions of equations (Newton’s method), graphing. In the last few weeks of the course, we begin the study of integration (to be continued next semester in Math 34). Chapter 3 introduces the definite integral via Riemann sums, together with some applications to physics and finding areas under curves. Finally, in chapter 6 we reach the Fundamental Theorem of Calculus, which connects the definite integral with the process of differentiation.

A more detailed list of topics will be given on a weekly basis.

Exams and Quizzes: There will be three 1-hour, in-class exams. Dates: Friday, Sept. 24, Friday, Oct. 29, and Friday, Dec. 3. A cumulative final will be given at the time scheduled by the Registrar (Thursday, Dec. 16). Short quizzes will be given each Friday, except when an exam is given. Topics for exams and quizzes will always be announced well in advance. Calculators will be allowed on certain exams and quizzes, but not on others.

Assignments: Problem sets, consisting primarily of problems taken from the textbook, will be given weekly. Normally problems will be assigned on Friday and will be due the following Friday. Problems will be collected and (partially) graded. Collaboration on homework assignments is permitted, but don’t get into the habit of letting other people solve all the problems for you. Your homework should show the steps you take to arrive at the answers as well as the answers themselves.

Group Work: We’ll spend some time working in groups of 3-4 people on problems of various types. Some group assignments will be collected and graded, others will be less formal. Some of the group assignments will involve work in the computer lab. (No previous computer experience is necessary). I’ll choose the groups randomly at first, then shuffle them later in the semester. Most people find working in groups to be an effective and enjoyable way to learn. To make the most of it requires the attendance and participation of everyone.

General Format: Monday, Tuesday, and Wednesday classes will generally be devoted to lecture and group assignments. Thursdays will be devoted to answering questions on the current assignment, which will be due Friday. Quizzes and exams are given on Fridays. After quizzes on Fridays we will review the quiz and perhaps begin some new material.

Grading:

Problem Sets  10 @ 10 pts. each  100 pts.
Midterm exams  3 @ 100 pts. each  300
Quizzes  10 @ 10 pts each  100

Final Exam 100 Group work, attendance and participation 100 Total 700 pts.

The course grade will be based on the overall distribution of points in the class - for example, if the class average is 500 points, this will probably be equivalent to a grade in the low B range.

Help: My office is SW318, phone 793-2459. Office hours are Monday-Thursday 11:00-12:00, and Monday-Tuesday 2:00-3:00, or by appointment - call, email me, or see me after class.

The Calculus Workshop is described on the attached sheet. Many students have found this to be very helpful.

Mike Elkas ‘00, a math major, will be the teaching assistant for Intensive Calculus this year. He will grade the homework, help out in class with the group discussions, hold review sessions, and occasionally be available outside of class, e.g., in the Calculus Workshop before exams.

Advice:

Most people find it handy to have a calculator, although I don’t require it. A decent graphing calculator is a good investment for this and your other science courses.

Take notes and use them. This may seem obvious, but many people diligently copy down everything on the board, and then never look at it again. Used intelligently, your notes can be a valuable resource.

Read the book. You will probably find this textbook quite different from those you’ve worked with in previous math courses. The emphasis is on conceptual understanding. Many of the problems are open-ended and require you to think creatively about the material.

Try to set up a regular study schedule and work at a steady pace. It’s not easy to play catch-up in a mathematics course, since every day builds on the previous one. Do a few problems, a little reading and reviewing of notes every day. If you are having trouble, get help as soon as possible.